RULE. The burtlens of similar built ships are to each other, as the cubes of their like dimensions. EXAMPLE. If a ship of 300 tons burthen be 75 feet long in the kcel, I demand the barthen of another ship, whose keel is 100 teet long ? As 75x75x75:300 : : 100 x 100 x 100 :711 2 0 24+ T. cwt. qrs. lb. OR DUODECIMALS, CROSS MULTIPLICATION, IS a rule made use of by workmen and artificers in cast ing up the contents of their work. RULE. 1. Under the mulplicand write the corresponding deno minations of the multiplier. 2. Multiply each term into the multiplicand, beginning at the lowest, by the highest denomination in the multiplier and write the result of each under its respective term; ob serving to carry an unit for every 12, from each lower dc. nomination to its next superior. 3. In the same manner multiply all the multiplicand by the inches, or second denomination, in the multiplier, and set the result of each term one place removed to the righi hand of those in the multiplicand. 4. Do the same with the seconds in the multiplier, setting the result of each term two places to the right hand of those in the multiplicand, &c. EXAMPLES. 4 6 9 7 5 8 97 N N 11 FEET, INCHES AND SECOxps. F. 1. Multiply 9 8 6 Bý 7 I 3 (tiplicf, 67 11 6 =prod. by the feet in the mul7 3 4 6 ditto by the inches. 2 5 1 6 =ditto by the seconds. How many square feet in a board 16 feet 9 inches long, ind 2 feet 3 inches wide ? By Duodecimals. By Decimals. F. 1. 16 9=16,75 feet. 2 3 2 3=2,25 33 6 8375 3350 3850 i F. . AN 376875-87 & 8 Ans. 37 TO MEASURE LOADS OF WO01), RULE.-Multiply the length by the breadth, and the product by the depth or hoight, which will give the content in solid feet; of which 64 muke half a cord, and 128 a cord. EXAMPLE. How many solid feet are contained in a load of wood. 7 feet 6 inches long, 4 feet 2 inches wide, and 2 feet 3 inches high? 7 ft. 6 in.=7,5 and 4 ft. 2 in. -4,167 and 2 st. 3 in = 2:15; then, 7,5 x 4,167=31,2525 X2,25=70,318125 solid feet, Ans. But loads of wood are commonly estimated by the foot, allowing the load to be 8 feet long, 4 feet wide, and then 2 feet high will make half a cord, which is called 4 feet of wood; but if the breadth of the load be less than 4 fect, its height must be increased so as to make half a cord, wnich is still called 4 feet of wood. By measuring the breadth and height of the load, tlie content may be found by the following RULE.-Multiply the breadth by the height, and half the product will be the content in fect and inches. EXAMPLE. Required the content of a load of wood which is 3 feet 9 inches wide and 2 feet 6 inches high. By Duodccimals. By Decimals. F. in. F. 3 9 3,75 2 6 2,5 9 4 6 9,375 F. in. Ans 4 8 3 4,68754 87 or half a cord and I inches over. The foregoing method is concise and easy to those who are wod acquainted with Dnodea nals, but the following table will give ha content of any load of wood, by inspection only, sufficiently exact for eommon practice ; which will be found ver konvenient. A TABLE vf Breadth, Height, and Conteni. Inches. 123|4 1 2 3 4 5 6 7 8 9 10 11 2 6 15 30/45/60 1 2 4 5 6 7 9 10 11 12 14 7 1631 4762 1 3 4 6 8 9 10 12 13 14 8 16 32 48 64 11 3 4 5 7 8 9111211315 9 1733 49,66 1 31 41 6 7 8 91112 14 15 10 173451 68 3 4 6 7 9 10 11 13/14/16 11 ||1835 53 70 3 4 6 7 9 10 12 13 15 16 3 0 18365472; 3 51 5 6 8911 12 14 15117| 1 1937 56,74 3 51 6 81 911 12 14 16 17 2 | 1938 57176 3 5 6 8 10/11/13/14, 16/17 3 1939 5978 2 3 5 7 8 1011 13151618 4 ||201406080 2 3 5 7 8 10 12 13 15 17 18 5 121416282 2 3 5 7 8 10 12 14 16 17:19 6 ||21|4263 84|| 2 41 5 7 9 11 12 14 16 18 19 7 || 22 43 64 86 2 4 5 7 9 11 13 14 16 18 20 8 422 44 66 88 2 4 6 7 9 11 13 15 17 18 20 9 |23 4568 90 2 4 6 7 9 11 13 15 17 1921 10 ||23 166992 2 4 6 7 9 12 13 15 17 19 21 11 2347,70 91 2 4 6 8 10 12 14 16 18 20 22 4 O ||24|48 72 96 2 4 6 8 10 12 14 16 18 20 2.2 TO USE THE FOREGOING TABLE. First measure the breadth and height of your load to the nearest average inch; then find the breadth in the left hand column of the lable, then move to the right on the same line till you come under the height in feet, and you will have the content in inches, answering the feet, to which add the content of the inches on the right and divide the sum by 12, and you will have the true content of the load in feet and inches. Note.-The contents answering the inches being always small, may oe added by inspection. EXAMPLES. 1. Admit a load of wood is 3 scet 4 inches wide, and 2 feet 10 inches nigh, required the content. Thus, against 3 feet 4 inches, and under 2 feet, stands 40 inches; and under 10 inches at top, stands 17 inches: then 40+17=57, true content in inches, which divide by 12, gives 4 feet 9 inches, the answer. 2. The breadth being 3 fect, and height 2 feet 8 inches; required the con Sthing with breadth 3 fret inches, cuind under 2 feet alop, stands 36 mches ; and under 8 iuclies, stands 12 inches : now 36 and 12 make 46, the answer in mches; and 48:13—4 feel, or just half a cord. 3. Admt the breadih to be 3 feet Il inches, and height 3 feet 9 inches; eynired the conteni. Unde: 3 feel at top, slands 70; and under 9 inches, is 18 : 70 and 18, make $8:12=7 cel 4 inches, or ti. I qr. 2 inches, the answer. TABEI. Showing the amount of £l, or $1, at 5 and 6 per cent. pe annum, Compound Inter 'st, for 20 years. | Yrs.5 per cent. 6 per cent.| Yrs. 5 per cent. 6 per cent. 1 1,05000 1,06000 11 1,71034 1,89329 2 1,10250 | 1,12360 12 1,79585 2,01219 3 1,15762 1,19101 13 1,88565 2,13292 4 1,21550 | 1,26247 14 1,979932,26090 5 1,27623 | 1,33322 15 2,07893 2,39655 6 1,34009 | 1,41851 16 2,18287 2,54727 1,40710 | 1,50363 17 2,29201 2,69277 8 1,47745 1,59384 18 2,40661 | 2,85433 9 1,55132 1,68947 19 | 2,52695 3,02559 10' 1,62889 | 1,79084 20 2,65329 3,20713 VII. The weights of the coins of the United States. prot. grs. Eagles, 11 Standard 5 15 Gold. 2 1941 17 Half-Dollars, 8 16 Standard 4 8 Silver. 1 173 204 Cents, 8. 16 Copper. 4 8 The standard for gold coin is 11 parts pure gold, and ane part alloy-the alloy to consist of silver and copper. The standard for silver coin is 1485 parts fine to 179 paru alloy-the allov to be wholly copper. |